Irregularity and singular vector growth of the differentially heated rotating annulus flow

The problem of weather prediction is to a large part determined by the large-scale atmospheric flow. This flow is irregular but not fully turbulent. The irregularity can be related to instability, nonlinear wave-wave interactions, or randomly excited singular vectors. In the present study, the latter mechanism is investigated numerically and experimentally. For this purpose, a baroclinic quasigeostrophic low-order model is adjusted to a differentially heated rotating annulus experiment, an established laboratory analog to the atmospheric circulation. We linearize the low-order model about a time-mean state to study the growth of singular vectors and compare those with singular vectors that have been derived empirically from the experimental data. Qualitative agreement of the numerically and experimentally derived singular vectors form the basis for a deeper analysis of the low-order model. In particular, for a broad range of annulus rotation frequencies and radial temperature differences, we compute the maximal growth rates of the low-order model. These growth rates are displayed as a function of the Taylor and thermal Rossby number, a frame widely used in studies of annulus regime transitions. We can show that most regime transitions defined by E.N. Lorenz in the sixties have their counterpart in the Taylor-Rossby singular value diagram. Most striking is the fact that for the irregular regime by far, the largest growth rates can be found. We suppose that irregularity in the transition region to geostrophic turbulence might for some part result from randomly excited singular vectors with unusual large growth rates. In concert with nonlinear wave-wave coupling, this process might explain the gradual broadening of the wave spectrum that has been found for the route to geostrophic turbulence in annulus flows.